On the Variational Regularity of Cameron-Martin paths
Probability
2013-11-01 v2
Abstract
It is a well-known fact that finite rho-variation of the covariance (in 2D sense) of a general Gaussian process implies finite rho-variation of Cameron-Martin paths. In the special case of fractional Brownian motion (think: 2H=1/rho), in the rougher than Brownian regime, a sharper result holds thanks to a Besov-type embedding [Friz-Victoir, JFA, 2006]. In the present note we give a general result which closes this gap. We comment on the importance of this result for various applications.
Keywords
Cite
@article{arxiv.1305.2943,
title = {On the Variational Regularity of Cameron-Martin paths},
author = {Peter K. Friz and Benjamin Gess and Sebastian Riedel},
journal= {arXiv preprint arXiv:1305.2943},
year = {2013}
}
Comments
The contents of this paper are now included in arXiv:1307.3460